A massive single-input multiple-output (SIMO) system with a single transmit antenna and a large number of receive antennas in intersymbol interference (ISI) channels is considered. Contrast to existing energy detection (ED)-based non-coherent receiver where conventional pulse amplitude modulation (PAM) is employed, we propose a constellation design which minimizes the symbol-error rate (SER) with the knowledge of channel statistics. To make a comparison, we derive the SERs of the ED-based receiver with both the proposed constellation and PAM, namely Pe_opt and Pe_pam. Specifically, asymptotic behaviors of the SER in regimes of a large number of receive antennas and high signal-to-noise ratio (SNR) are investigated. Analytical results demonstrate that the logarithms of both Pe_opt and Pe_pam decrease approximately linearly with the number of receive antennas, while Pe_opt degrades faster. It is also shown that the proposed design is of less cost, because compared with PAM, less antennas are required to achieve the same error rate.
@article{arxiv.1809.02946,
title = {Non-coherent Massive SIMO Systems in ISI Channels: Constellation Design and Performance Analysis},
author = {Huiqiang Xie and Weiyang Xu and Wei Xiang and Ke Shao and Shengbo Xu},
journal= {arXiv preprint arXiv:1809.02946},
year = {2019}
}